The original WoW was painful. Mobs took forever to die; one additional enemy in a fight was a pain, two probably meant death. There was a ton of running. Most buffs lasted two minutes, many took reagents, abilities were trained and often out of reach if you lacked the necessary gold. Warlocks had to farm shards, hunters had to carry ammo -- even my warrior did, since in vanilla WoW she can carry a bow and fire arrows herself.
Most profitable professions are considered to be Herbalism and Enchanting in pair. You can have Enchanting only for Disenchanting skill, it will bring decent gold. Consider the fact of disenchanting all soulbound armor, not just selling them to a vendor, but I do not recommend to disenchant any kind of weapons, it is more profitable to sell it to a merchant if it is a soulbound item, or sell it on auction house if it is BoE (bind on equip).
Keep in mind that these quests are optional, and are not necessary to continue leveling and capturing companions. They are also account-wide, so if you complete the quest chain on one character, you will not be able to complete it again on another. However, any progress that you've made will be saved and you can pick up where you left off in the quest chain on another character. The dailies that you've unlocked will also be accessible by all your toons.
A new quest will pop up once your first pet reaches level 3. It will send you to either Audrey Burnhep in Stormwind or Varzok in Orgrimmar. These trainers will offer a quest chain to battle specific Pet Tamer NPCs on each continent. Defeating each of these NPCs will reward a nice chunk of experience for your pets, as well a Sack of Pet Supplies (which has the chance to drop the Porcupette companion, among the always-useful pet bandages).
For example, the Azure Whelpling belongs to the Dragonkin family. However, it has Beast, Magic, and Elemental abilities in addition to a Dragonkin attack. Different attacks are strong and weak against different family types. Having a diverse spell selection might increase your chances of being prepared with a strong attack against an opposing team.
I recreated my very first character -- a human warrior, because in the last-push alpha test I joined in 2004, there was no Horde -- and logged in. Immediately, I was surprised by how good the graphics actually looked, for being 15 year old textures-on-polygons. Warcraft's bright colors and cartoony aesthetic continue to this day, so all the increased resolution and better-contoured characters in Lordaeron don't really change the game's visual aesthetic.